In the javelin throw at a track-and-field event, the javelin is launched at a speed of 29 m/s at an angle of 36 degrees above the horizontal. As the javelin travels upward, it’s velocity point above the horizontal at an angle that decreases as time passes. How much time is required for the angle to be reduced from 36 degrees at launch to 18 degrees?

1 answer

y = 29 sin36° t - 4.9t^2 = 17.045t - 4.9t^2
x = 29 cos36° t = 23.461t
at any point in flight, tanθ = dy/dx = (dy/dt) / (dx/dt)
So, you just need to find when

(17.045 - 9.8t)/23.461 = tan 18°